Optimizing the drying parameters of a fixed bed with ...

September, 2021 Int J Agric & Biol Eng Open Access at https://www.ijabe.org Vol. 14 No. 5 255

Optimizing the drying parameters of a fixed bed with reversing ventilation

for peanut using computer simulation

Jianchun Yan, Huanxiong Xie*

, Hai Wei, Huichang Wu, Zhaoyan You (Nanjing Institute of Agricultural Mechanization, Ministry of Agriculture and Rural Affairs, Nanjing 210014, China)

Abstract: To obtain the optimal operation parameters of fixed-bed reversing ventilation drying of peanuts, a set of partial

differential equations indicating the heat and mass transfer relationships between the peanut pods and air during drying was

proposed. Then, a series of discretized models were established for simulation, and the time consumed, unevenness, and

energy consumption for batch drying were calculated. The results showed that reversing ventilation and segmented drying

was helpful to these issues for high drying ability. The optimal operation parameters were determined by uniform design

experimentation of mathematical simulation. The result showed that when the moisture content (wet basis) was above 22%, a

ventilation velocity of 0.46 m/s was optimal; when the moisture content was between 8% and 22%, a ventilation velocity of

0.20 m/s was optimal. Using the optimal parameters, the computer simulating result was compared with the experimental

results. The correlation coefficients between the simulating and the experimental values for the temperature and moisture

content were all above 0.98 and the quality of dried peanuts was close to that of natural sun-dried ones, which indicates that the

optimization results of the drying parameters are highly reliable.

Keywords: peanut, fix bed drying, reversing ventilation, simulation, optimization

DOI: 10.25165/j.ijabe.20211405.6354

Citation: Yan J C, Xie H X, Wei H, Wu H C, You Z Y. Optimizing the drying parameters of a fixed bed with reversing

ventilation for peanut using computer simulation. Int J Agric & Biol Eng, 2021; 14(5): 255–266.

1 Introduction

Peanut is the dominant high-quality oil-bearing crop and an

important food protein resource in China. For the past decade,

China has been the largest peanut producer and has the

second-largest planting area[1]. Influenced by agricultural policy,

population mobility, and land transfer, the mechanized harvesting

of peanuts has increased over years; consequently, harvesting is

synchronized, and fresh peanut pods can be quickly amassed and

large amounts of peanuts wait for drying[2]. This rapid expansion

means that the drying facilities and labor available in rural areas

have not satisfied the demand for drying[2,3]. On overcast and

rainy days, mildew and rot of the crop usually occur, and aflatoxin

contamination is a relatively serious concern[4,5]. Economic and

practical peanut-drying methods are required. Some developed

countries with large-scale peanut planting, such as the United

States, have developed mature peanut drying technology and

equipment[6-8]. Peanut drying is usually divided into two stages:

first, vines are dried in the field after digging; second, centralized

drying is needed after pickup harvesting[9-12]. The entire drying

process is intrinsically combined with digging, picking, storage,

Received date: 2020-12-13 Accepted date: 2021-06-14

Biographies: Jianchun Yan, Assistant Professor, research interest: agricultural

products drying and processing technology, Email: [email protected]; Hai Wei,

Assistant Professor, research interest: agricultural products drying and

processing technology, Email: [email protected]; Huichang Wu, Professor, research interest: agricultural products processing technology, Email:

[email protected]; Zhaoyan You, Assistant Professor, research interest:

agricultural products processing technology.

*Corresponding author: Huanxiong Xie, Professor, research interest:

agricultural products processing technology. Nanjing Research Institute for

Agricultural Mechanization, Ministry of Agriculture and Rural Affairs, No.100,

Liuying, Xuanwu Disrict, Nanjing 210014, China. Tel: +86-25-84346256,

Email: [email protected].

and processing. When the dryer is loading, the moisture content

of peanuts (with their shells) is generally approximate to 20%.

During the drying process, the hot air generated by burning

liquefied petroleum passes through the material bed from the

bottom to the top[13,14]. Based on the material bed thickness and

initial moisture content, ventilation volumes are regulated to the

recommended values[7]. Although the above-mentioned two-stage

process has been widely used in the USA and Australia, in rural

China, little time is allowed for the crop to be dried before the next

crop is planted. To increase farm productivity, the drying of fresh

peanut pods is a priority[3,15]. However, owing to the large

moisture content reduction required, the drying effect of the

above-mentioned method used in the USA is poor. In addition,

high energy and equipment price has made the peanut drying

expensive and promoting fresh peanut drying difficult in rural

China. Generally, peanut farmers use the fixed-bed dryers as

supplementary or emergency means of drying[2]. However,

uneven drying is a problem. To improve the uniformity of

fixed-bed drying, the fixed-bed reversing ventilation drying

technique for peanuts has been proposed. However, heat waste

during the middle and later stages of drying is a serious issue. It

is assumed for batch drying that the more uniform the drying is, the

more the air volume should be provided and the more energy is

consumed.

Numerical simulation has been widely used to describe the

drying process and develop production guidelines for peanuts and

other crops. Parti and Young[16] established a peanut bulk drying

model (PEADRY8), which was compared with the experimental

results for Virginia-type peanuts. The model took the peanut pod

as two separate components with moisture movement in both liquid

and vapor forms. Chai and Young[17] studied the effects of

airflow rate on drying times and costs of conventional and

recirculating peanut drying facilities using numerical simulation.

Yang et al.[18] studied the simulation of peanut drying in a

256 September, 2021 Int J Agric & Biol Eng Open Access at https://www.ijabe.org Vol. 134No. 5

trailer-type dryer with different thin-layer drying models and

equilibrium moisture contents. The result showed that the

Henderson-Pabis model using the Hummeida K-value and

modified Oswin EMC models provided the best fit with the

experimental data, although errors of temperature prediction

existed in the middle layer. Yan et al.[19] performed numerical

simulation on a barrel-shaped fixed bed and examined the drying

time, energy consumption, productivity, and uniformity under

different structures and ventilation parameters. Baker et al.[10]

proposed a drying rate control method (DRC1) for dryer heat

control, which was tested and compared with humidistat control

and conventional control methods using a bulk simulation model

and laboratory curing tests. Based on this foundation, Butts et

al.[13] improved the DRC1 and proposed the DRC2 control method.

Similar studies with grains, wheat, and maize have also been

conducted[20-24].

With reference to reversing ventilation drying, Ruiz-Lopez et

al.[25] developed a mathematical model to simulate the fixed-bed

drying of carrots with and without periodic reversals in the

airflow direction, and they found good agreement between the

experimental and predicted data. Khatchatourian et al.[26]

simulated the performance of cross-flow grain dryers with the

direction of airflow reversed with the grain flowing from top to

bottom. Yan et al.[27] performed numerical simulation of

fixed-bed wheat drying with periodic reversing ventilation, and

the optimal ventilation temperature and air velocity were

determined with the energy consumption cost as the index. Jia

et al.[28] experimentally investigated a fixed-bed drying method

that features with swing temperature and alternating airflow for

wheat drying and drew similar conclusions. Albini et al.[29]

evaluated barley drying in a fixed-bed dryer by either reversing

the airflow every 10 min or with no reversal. The results

showed that drying with an airflow reversal provided better

homogeneity; however, conventional drying led to improved

energy performance. Yan et al.[2] proposed a small-scale

reversing ventilation dryer for peanuts. Experiments with the

dryer showed that periodic reversing ventilation could effectively

improve drying uniformity, especially for high-moisture peanuts

with a moisture content of over 40%. From the above research,

numerical simulation and periodic reversing airflow appear to be

suitable methods for improving drying uniformity and optimizing

the drying process.

Thus, in this study, numerical analysis was used to calculate

the time consumption, moisture content difference, and thermal

energy consumption of batch peanut drying. The optimal drying

parameters were determined using the synthetic weighted mark

method to provide production guidance for peanut drying.

2 Materials and methods

2.1 Principle of reversing ventilation drying

Reversing ventilation drying is based on regular changes in

airflow direction in the air medium being dried to ensure that the

moisture content of different material layers in the vertical

direction is approximately equal after drying. At the beginning of

drying, hot air enters the lower air chamber, passes through the

material layers being dried upward, enters the upper air chamber,

and finally discharges exhausts from the drying chamber into the

atmosphere (Figure 1). After a while, when an obvious moisture

content gradient in the material bed is formed, the ventilation

direction changes. Air enters the upper air chamber first, passes

through the material layers downward, enters the lower air chamber,

and finally discharges exhausts into the atmosphere. After drying

for a period, when the original gradient has been eliminated and a

new gradient is formed, the ventilation direction is reversed again.

This process is repeated until the average moisture content reaches

8% wet basis to end the drying.

Material layer

Top air chamber

Inlet air

Outlet air

Lower air chamber

a. Ventilation from the bottom up

Material layer

Top air chamber Inlet air

Outlet air Lower air chamber

b. Ventilation from the top down

Figure 1 Principle of fixed-bed reversing ventilation drying

2.2 Drying model

2.2.1 Theoretical model of peanut drying

Peanut pods are generally composed of kernels and shells.

The moisture content of fresh peanuts after harvesting is often high

(approximately 40% wet basis or more). When harvesting, the

kernels are close to the inner walls of their shells; however, as the

moisture content of the pods gradually decreases during drying, the

gap between the shells and the kernels gradually increases,

hindering inward heat transfer and the outward mass transfer of

water. Additionally, the red coating that occurs on the seed and

white membranes on the inner wall of the shells hinder the outward

migration of moisture. Therefore, the heat and mass transfer of

peanut pods are complex; thus, it is difficult to construct a drying

model based on the characteristics of each component. In most of

the recent studies, peanut pods are regarded as cylindrical entities,

and the classic semi-empirical thin-layer drying equations are

generally fitted to the experimental data[18,30].

In this study, based on previous studies on peanut thin-layer

drying[30], and simulating fixed-bed drying using partial differential

equations (PDEs), the following assumptions of the heat and mass

transfer were made to simplify the calculations: the temperature

gradient inside a single peanut pod was neglected, heat conduction

between peanut pods was neglected, dryer wall was insulated, and

its heat capacity was ignored; a sufficiently short time interval was

considered, and the specific heats of wet air and peanut pods were

regarded as constant[21,27,31].

According to the basic theory, heat and mass transfer between

peanut pods and air in the material bed can be described by a series

of PDEs for balancing air mass, air heat, peanut pod heat, and

peanut pod mass. Based on the assumptions stated above, they

are shown as Equations (1)-(4), which are widely used in the drying

of granular agricultural products[8,27,31]. Equation (4) is the

thin-layer drying equation for peanut pods, which was obtained in

previous studies[30]. In these studies, several semi-empirical

thin-layer drying models were compared with peanut pod

thin-drying experimental data by regression analysis, and the

results showed that the diffusion–approximation model was the

most suitable for thin-drying peanut pods using hot air.

pba

a

( , ) ( , ) ( , )H x t V H x t M x t

t x t

(1)

September, 2021 Yan J C, et al. Optimizing the drying parameters of a fixed bed with reversing ventilation for peanut Vol. 14 No. 5 257

a T s

a a v

( , ) ( , ) ( ( , ) ( , ))

( ( , ) )

T x t V T x t h a T x t x t

t x c H x t c

(2)

ga vT s

pb pb w pb w

( ( , ) ( , ))( ( , ) ( , )) ( , )

( ( , )) ( , )

h c T x t x th a T x t x t M x t

t c c M x t c c M x t t

(3)

e

e

( , ) ( , )e (1 )e

( ,0) ( , )

kt kbtM x t M x ta a

M x M x t

(4)

where,

a

a

a a

2a

0.75246 0.081968 ( ) 0.0095385 ( , )

0.0018244 ( ) ( , )

0.058862 - 0.098516 ( ) 0.0023255 ( ) ( , )

3.09066 0.72825 ( ) 0.19585 ( , ) 0.0035682 ( , )

a V t T x t

V t T x t

b V t V t T x t

k V t T x t T x t

25°C≤T≤50°C, 0.2 m/s≤Va≤1 m/s.

and x is the depth of the bed from the bottom, m; t is the drying

time, h; M is the moisture content (dry basis) of peanuts, kg/kg; θ is

the temperature of peanuts, °C; H is the absolute humidity of the

medium air, kg/kg; T is the temperature of the air medium, °C; Va

is the medium air velocity, m/s; ρpb is the bulk density of peanut

bed, kg/m3; ρa is the density of dry air, kg/m3; ε is the porosity of

peanut bed; ca is the specific heat of dry air, J/(kg°C); cv is the

specific heat of water vapor, J/(kg°C); cw is the specific heat of

liquid water, J/(kg°C); cpb is the specific heat of bulk peanuts,

J/(kg°C); hT is the heat transfer coefficient, W/(m2°C); hga is the

gasification heat of the water in peanuts, J/kg; a, b, and k are the

drying constants; Me is the equilibrium moisture content of peanut

pods, kg/kg; as is the specific surface area of peanuts, m2.

2.2.2 Discretization of PDEs in the model

For the convenience of calculation, the material bed was

considered as composing of several horizontal thin layers, with

each thin layer regarded as a node. The drying time was divided

into several equal parts based on the drying time sequence, and

each part was regarded as a node. For upward ventilating, the

simulation started from the bottom of the fixed bed. For

downward ventilating, the simulation started from the top to the

bottom of the fixed bed. The moisture contents and temperatures

of the nodes for the material layers and the medium air passing

through the material layers at different position were calculated.

The calculation results were used as the input for the next node,

and then the variables at the next node were calculated. This

process continued until the average moisture content of peanuts in

the total material bed reached the storage requirement[32].

The material bed was divided into several units along the

thickness direction, where each unit was Δx m, x =i·Δx (i is the

number of thickness units), and the total thickness was m·Δx. The

drying time was also divided into several sections, and each section

was Δt h, t = j·Δt (j is the number of time units). The simulation

was terminated when the average moisture content of the material

bed reached the terminating (required) moisture content. Based

on the sequence of hot air passing through the divided layer (for

upward ventilation, the ith layer peanut was dried first, and the

(i+1)th layer was dried later; In the case of downward ventilation,

the (i+1)th layer peanut was dried first, and the ith layer peanut was

dried later.), the PDEs in the model were discretized for the two

ventilation conditions using the finite difference method. After

simplification and arrangement, the following equations are

obtained:

For upward ventilation:

1, 1 1, 1, 1 , 1 pb , 1 ,a

a

i j i j i j i j i j i jH H H H M MV

t x t

(5)

1, 1 1, 1, 1 , 1 T s 1, 1 , 1a

a a 1, 1 v

( )

( )

i j i j i j i j i j i j

i j

T T T T h a TV

t x c H c

(6)

, 1 ,

T s 1, 1 , 1 ga v 1, 1 , 1 , 1 ,

pb pb , 1 w pb , 1 w

( ) ( )

( )

i j i j


i j i j

t

h a T h c T M M

c M c c M c t

(7)

, 1 , , 1 , 1 ,( ) ( ), 1 , 1 , 1

,0 e , 1 e , 1

( e (1 )e )

( )

i j eq i j i j i j eq i jk t t k b t ti j i j i j

i i j i j

M a a

M M M

(8)

where,

, 1 a , 1 a , 10.75246 0.081968 0.0095385 0.0018244i j i j i ja V T V T

, 1 a a , 10.058862 0.098516 0.0023255i j i jb V V T

2, 1 a , 1 , 13.09066 0.72825 0.19585 0.0035682i j i j i jk V T T

For downward ventilation:

, 1 , , 1 1, 1 pb 1, 1 1,a

a

i j i j i j i j i j i jH H H H M MV

t x t

(9)

, 1 , , 1 +1, 1 T s , 1 +1, 1a

a a , 1 v

( )

( )


i j

T T T T h a TV

t x c H c

(10)

+1, 1 +1,

T s , 1 +1, 1 ga v , 1 +1, 1 +1, 1 +1,

pb pb +1, 1 w pb +1, 1 w

( ) ( )

( )

i j i j


i j i j

t

h a T h c T M M

c M c c M c t

(11)

+1, 1 eq +1, +1, 1 +1, 1 eq +1,( ) ( )+1, 1 +1, 1 +1, 1

+1,0 e +1, 1 e +1, 1

( e (1 )e )

( )

i j i j i j i j i jk t t k b t ti j i j i j

i i j i j

M a a

M M M

(12)

where,

+1, 1 a +1, 1

a +1, 1

0.75246 0.081968 0.0095385

0.0018244

i j i j

i j

a V T

V T

+1, 1 a a +1, 10.058862 - 0.098516 0.0023255i j i jb V V T

2

1, 1 a 1, 1 1, 13.09066 0.72825 - 0.19585 0.0035682i j i j i jk V T T

2.2.3 Initial and boundary conditions

It was assumed that, before drying, the initial moisture content

of peanuts is M0 (dry basis), and the initial temperature of peanuts

is θ0. The temperature of the input air for drying is Tin, and the

absolute humidity of the input air is Hin. Thus, the initial

conditions are:

,0 0

,0 0

i

i

M M

, 0 i m (13)

where, m is the maximum node number of the bed thickness.

The boundary conditions with upward ventilation are:

0, in

0, in

j

j

H H

T T

,

ex ex ex ex2( 1) (2 1)N t N tj

t t

(14)

where, tex is the interval time of each airflow direction reversal, and

Nex is the number of ventilation cycles. Each cycle includes

upward ventilation time and downward ventilation time, with a

duration of 2tex.

For downward ventilation, the boundary conditions were:

, in

, in

m j

m j

H H

T T

,

ex ex ex ex(2 1) 2N t N tt

t t

(15)

2.2.4 Equivalent drying time

For drying simulation, the material bed was divided into

several thin layers along the thickness direction. The heat of the

medium air was absorbed, and the air was cooled by the front layer

materials before passing through the inner layer materials, which


belonged to the variable temperature drying category. When

calculating the moisture content, the drying time cannot be directly

substituted into Equation (8) or (12). The equivalent drying time

must be solved which corresponded to the layer material moisture

content of the previous time node under the current drying

temperature and air velocity[19].

The optimization function “fminsearch” of Matlab 2019a

(MathWorks, Natick, Massachusetts, USA) was used to solve the

equivalent drying time. Specific methods were as follows: set

function F = |M(teq) – Mi,j|, where, teq is the equivalent drying time, h;

Mi,j has been solved in the previous loop; M(teq) is the solution after

substituting teq into Equation (8) or (12). When the function F

reaches its minimum value (approaching 0), the value of teq is the

equivalent drying time corresponding to the ith layer moisture

content Mi at time t = j·Δt.

2.2.5 Other auxiliary equations and physical parameters

The simulation accuracy of drying mainly depends on the

values of the coefficients and parameters of the model, such as the

convective heat transfer coefficient, vaporization heat, and

equilibrium moisture content. Detailed studies of these

parameters have been conducted using experiments and empirical

or semi-empirical equations.

Bitra et al.[33] summarized the bulk density of peanut pods

under different moisture contents and obtained the following

empirical equation: 2

pb db db0.0034 0.0480 216.06M M , db0 25M (16)

where, Mdb is the dry basis moisture content of peanut pods, kg/kg.

Setting Mdb= 0, the bulk density of dry peanuts is 216.06 kg/m3.

Wright and Porterfield[34] studied the relationship between the

specific heat and moisture content of bulk peanuts and obtained a

semi-empirical equation: 0.881

pb db1.687 1.779c M , db0 25M (17)

Setting Mdb = 0, the specific heat of dry bulk peanuts is 1.686

kJ/(kg°C).

Yan et al.[19] simplified the calculation equation of the

convective heat transfer coefficient between the peanut pods and

the medium air and obtained the semi-empirical equation: 21

32T A A A A192.28( ) 210.02( )h (18)

where, ρA is the density of the medium air, kg/m3; μA is the average

velocity of the medium air, m/s.

Correa et al.[35] studied the heat of water vaporization in peanut

pods and provided the following equation:

ga e1000 (1691.86exp( 0.24 ) 2400.43)h M , e0 20M (19)

Chen[36] studied the equilibrium moisture content (dry basis) of

peanuts under various temperature and humidity conditions and

obtained a semi-empirical equation for the equilibrium moisture

content of peanut pods:

1

2.5404

e ( , ) (6.8229 0.017698 ) ,1

RHM x t T

RH

5 C 45 C 10% 95%T RH , (20)

where, RH is the relative humidity of the air, %.

Other physical parameters of the air used in the simulation are

listed in Table 1, and the data were from Mujumdar[8].

2.3 Evaluation indices

2.3.1 Time consumption

The time consumed was the time of drying until the average

moisture content of the peanut material bed reached its termination

moisture content.

Table 1 Physical parameters of hot air used in the simulation

Physical parameters Symbols Values

Specific heat of dry air/(kJ·kg-1

·°C-1

) ca 1.006

Specific heat of water vapor/(kJ·kg-1

·°C-1

) cv 1.863

Specific heat of liquid water/(kJ·kg-1

·°C-1

) cw 4.195

Density of dry air/kg·m-3

ρa 101.325

0.287( 273.16)T

Note: T is the temperature of the drying air, °C.

tfinal = (jfinal + 1)Δt (21)

where, tfinal is the total elapsed time for batch drying, h; jfinal is the

last iteration of the time node.

2.3.2 Moisture content difference

The moisture content difference was obtained based on the

simulation results, which could be calculated by subtracting the

minimum moisture content from the maximum moisture content of

the material layers at a specified drying time.

Mun = max(M(x,tc)) – min(M(x,tc)) (22)

where, Mun is the moisture content difference, and tc is the specified

time during drying.

2.3.3 Energy consumption per unit mass

Practically, energy is mainly consumed in batch drying as heat,

since the energy consumed by the fans supplying fresh air is small

and can be ignored[37]. The energy consumption of batch drying

can be obtained by:

final

co a a a v in in am0

( )( ( ))( ( ) ( )) dt

E V t c c H t T t T t S t (23)

where, Tam is the ambient temperature, °C; Eco is the energy

consumption, J; and S is the loading area, m2.

The energy consumption per unit mass of dried peanuts can be

obtained from the quotient of the energy consumption of batch

drying and the final mass of materials at the end of drying.

copum

final

EEm

(24)

where, Epum is the energy consumption per unit mass of dried

peanuts, J/kg; and mfinal is the mass of dried peanuts, kg.

The mass of the material at the end of drying can be obtained

using Equation (25):

mfinal = Shρbf (25)

where, h is the height of the material bed, m; and ρbf is the bulk

density of the dried peanuts, kg/m3.

2.3.4 Synthetic index

To obtain the optimal drying operation parameters, the

synthetic weighted mark method[38,39] was used to transform

multiple performance indices into a single index, which was used

for optimization analysis.

(1) Determining the weight of each index

The drying time, moisture content difference, and energy

consumption per unit mass of dried materials are important indices

for evaluating drying performance. The moisture content

difference is an index used to evaluate the quality of the drying

operation. The drying time and energy consumption are indices

used to reflect the drying cost. Therefore, the weights W1, W2, and

W3 of the time consumed, moisture content difference, and energy

consumption per unit mass of the material were set to 0.25, 0.5, and

0.25, respectively, based on experience.

(2) Unifying the change trends of each index

To ensure that the greater the value of the synthetic weighted

mark, the better the drying, the “smaller the better” of indices

should be converted into the “larger the better” and the sign of

indices should be adjusted accordingly. Therefore, the time


consumed, moisture content difference, and dry material per unit

mass were all negative. Thus, *

1, 1,J JY Y , *2, 2,J JY Y , *

3, 3,J JY Y , J =1, 2, …,13 (26)

where, for step J, Y1,J is the simulated index value of the time

consumed, Y2,J is the simulated index value of the moisture content

difference, and Y3,J is the simulated index value of the energy

consumption per unit mass of the material.

(3) Unifying the order of magnitude and dimension of each

index

To eliminate the influence of the order of magnitude and

dimension of each index (the magnitude and dimension of Y *1,J

was “h”; the magnitude and dimension of Y*2,J was “%”; and the

magnitude and dimension of Y *3,J was “×106 J/kg”) on its weighted

mark value and make the weighted mark value of each index

comparable, it was necessary to unify the order of magnitude and

dimension of each index. The no-magnitude and dimensionless

marks of each index were obtained from Equation (27): * *, ,min**

, * *,max ,min

( )100 , 1,2,3; 1,2, ,13

( )

I J II J

I I

Y YY I J

Y Y

(27)

where, Y**I,J is the score of the Ith index of Jth simulation results,

Y*I,J is the Ith index value of the Jth simulation results after unifying

the trends, Y*I,max is the maximum value of the Ith index after

unifying the trends and Y*I,min is the minimum value of the Ith index

after unifying the trends.

(4) Calculating synthetic weighted mark Y*J

The synthetic weighted mark is the sum of the weighted marks

of each index and is obtained from Equation (28):

* *, ,min**

, * *,max ,min

( )100 , 1,2,3; 1,2, ,13

( )

I J II J

I I

Y YY I J

Y Y

(28)

where, for step J, Y*J is the comprehensive weighted score of the

simulation results, and WI is the weight of index I.

2.4 Simulation and parameter setting

Matlab 2019a software was used to simulate the reversing

ventilation drying process of a peanut bed. Based on the

equations in sections 2.2 and 2.3, the simulation program was

compiled to calculate teq, Mi,j, θi,j, Hi,j, Ti,j, tco, Epum, and Mun. A

flowchart of the simulation program is shown in Figure 2.

Based on the applicability of the thin-layer drying equation[30],

the thickness of the thin-layer unit Δx = 0.03 m and the time unit

Δt = 0.1 h. Based on the long-term storage conditions used for

peanuts[32], the moisture content of peanut pods should be generally

lower than 8% (wet basis). Therefore, the termination moisture

content for the simulation calculation was set to 8%.

Based on previous studies on fixed-bed peanut drying, the

input temperature of medium air should not exceed 38°C[13,19];

otherwise, it will affect the quality of peanuts. Therefore, the

input temperature of the medium air was set to 38°C. For

high-moisture peanut pods, a large thickness of the material bed

can easily cause mildew and uneven drying. Based on the studies

performed by Cundiff and Baker[7], the recommended thickness of

the peanut bed for the traditional fixed-bed drying method ranges

from 0.9 to 1.8 m when the moisture content of the wet basis

ranges from 20% to 40%. Owing to the effects of enhancing

drying uniformity for airflow reversal in fixed-bed drying, the

depth of the peanut bed was set to 1 m. To simplify the

calculation, the average ambient temperature was set to 25°C,

humidity during the harvesting period was set to 50%, and moisture

content of peanuts in the main production area was set to 40% wet

basis.

Figure 2 Flowchart of the computer program for the simulation of

fixed-bed reversing ventilation drying (Symbols are given in the

nomenclature)

2.5 Verification method and materials

2.5.1 Experimental equipment and materials

To verify the accuracy of the computer simulation, a

self-developed 5H-5A peanut reversing ventilation dryer (Figure 3)

was used for the experiment.

a. Prototype dryer

b. Experimental process

Figure 3 5H-5A peanut reversing ventilation dryer

The equipment is comprised of a drying box, heat pump, fan,

ventilation devices, air uniform mechanism, and control system.

The temperature of hot air entering the drying box could be

adjusted to provide a constant temperature under an ambient


temperature up to 20°C, with an accuracy of ±1°C. The

maximum ventilation capacity was approximately 24 000 m3/h, and

the fan motor speed was adjusted by the frequency converter, with

an accuracy of ±0.1 Hz. The material-loading area of the drying

chamber was 12 m2 (6 m×2 m), maximum loading thickness was

1 m, the distance between the loading punching plate and the floor

of the bottom air chamber was 450 mm, and minimum distance

between the top of the material layer and the cover was 450 mm.

Peanuts were harvested in Zhengyang County, Henan Province,

China, with an average moisture content of 40.8% (wet basis)

before drying. The average temperature and relative humidity of

ambient air were 24.1°C and 43.9%, respectively. The input

temperature of the drying air was set to 38°C, and the average air

velocity was regulated by a frequency converter based on the

experimental requirements.

2.5.2 Validation of simulation results

Peanut pods are characterized by large particle size and poor

fluidity; therefore, it is difficult to extract samples from the

material bed with a plug-in sampler to measure the moisture

content of the upper, middle, and lower layers of the material bed.

Therefore, a sampling cylinder was developed. The sampling

cylinder was a thin-walled cylindrical container with dense holes at

the bottom and wall (hole diameter, 5 mm; perforating ratio,

35.4%). The drying air entered and exited the container free from

the bottom and sidewalls. The diameter of the sampling cylinder

was 50 mm, and its height was 1000 mm.

To understand the changes in moisture content and temperature

in the upper, middle, and lower sections during drying, the volume

of peanuts was divided into 27 (3×9) test units in the horizontal

direction (Figure 4).

Figure 4 Schematic of testing area distribution

When loading materials, three sampling cylinders were placed

vertically at the center of each test unit, and the bottom of the

samplers was in contact with the porous bearing plate. As the

experiment continued, at 15 h, 30 h, and at the end of drying, one

sampling cylinder was removed from each test unit, and the

materials in the sampling cylinders were divided into three sections:

upper, middle, and lower section. The moisture contents of the

81 (3×27) testing points were then measured using the oven

method[40]. The moisture contents from the same height of the

layer materials were taken as a group, and the moisture contents of

the upper-, middle-, and lower-layer materials were calculated by

averaging each group.

Temperature sensors were placed at the center of each test unit

at the height of 165 mm, 500 mm, and 835 mm from the bearing

plate in the vertical direction. The number of temperature sensors

was 81 (3×27). The sensors of the same height of each test unit

were also taken as a group, and the average value of each group

was taken as the temperature value of the material in that layer.

The correlation coefficient was used to demonstrate the

statistical index of the relationship between simulating and

experimental values.

1

2 2

1 1

(Pr e Pr e)(Exp Exp)

(Pr e Pr e) (Exp Exp)

N

U U

U

N N

U U

U U

r

(29)

where, r is the correlation coefficient; PreU is the Uth simulation

prediction value; Pre is the mean of the predicted value; ExpU is

the Uth experimental value; and Exp is the mean of the

experimental value.

2.5.3 Quality tests of dried peanuts

When the drying process was completed, the dried peanuts

were discharged from their relevant ports and transported to a

designated area by the conveyor. In the process of peanut

discharge, a sample of peanuts was taken every 5 min. Five

samples were collected, and each sample had a mass of no less than

200 g. For every peanut sample, aflatoxin content was determined

based on ISO Standard 16050[41], the acid value was determined

based on ISO Standard 660[42], and the peroxide value was

determined based on ISO Standard 3960[43]. In addition, three

naturally dried peanut samples (total weight of samples was

approximately 3 kg, and the exposure time was approximately 5 d)

were selected as a control group, and the aflatoxin content, acid

value, and peroxide value of those samples were determined by the

same method. The flavor test was performed based on the ISO

Standard 6658[44].

3 Results and discussion

3.1 Numerical simulation

3.1.1 Peanut temperature and moisture content during drying

The temperature and moisture content (wet basis) of the

peanuts were simulated with an air velocity of 0.3 m/s, material bed

depth of 1 m, and airflow direction switching time of 3 h (Figure 5).

Owing to the ventilation sequence of the material layers changed

with air direction reversing each time, the temperatures of the

peanut layer at different heights gradually increased in a wave-like

shape with the increase in drying time. With the accumulation of

heat transferred from hot air to peanut layers and the reduction in

temperature difference between the material layers and hot air, the

fluctuation amplitudes gradually decreased as the temperature

approached the air input temperature. Because the bottom and top

materials were either the first or the last to contact hot air, the

temperature fluctuation amplitudes of the bottom and top materials

were the greatest. By contrast, the temperature fluctuation

amplitudes of the middle layers were small, because in the layers

near the middle position of the material bed, the ventilation

sequence changed mildly as the hot air direction changed. This

was similar to other results for airflow direction reversing

ventilation drying for carrots[25] and wheat[28].

In the initial stage of drying (0-3 h), air passed through the

material layer from the bottom to the top. As the air passed

through a critical position in the fixed bed, the relative humidity

was high sufficiently so that the moisture absorption balance was

achieved between the air and the layer material. Thus, the

moisture in the remaining material layers could not be absorbed.

When the ventilation direction was changed for the first time, the

upper material layers contacted hot air for the first time. The rate


of moisture decreased in the top layer material accelerated, whereas

the moisture content of the bottom layer changed mildly. The

moisture difference of the whole bed thus decreased rapidly, and

this process was repeated until the average moisture content reached

8% wet basis. Compared with traditional fixed-bed drying[21,22,25,31],

the periodic change in the airflow direction effectively reduced the

drying unevenness in the ventilation direction[25,27,29], which

reduced the moisture content difference by 70%-85%.

a. Temperature of the entire bed b. Moisture content of the entire bed

c. Temperature of five positions d. Moisture content of five positions

Note: The ambient air temperature was 25°C and humidity was 50%; the material bed depth was 1 m; Hot air input temperature was 38°C, air velocity was 0.3 m/s, and

the airflow reversing time was 3 h.

Figure 5 Variation of peanut material bed temperature and moisture content during the drying process

3.1.2 Average temperatures and moisture contents at different

ventilation velocities

The average (volume-averaged) temperatures and moisture

contents of the entire bed at different ventilation velocities were

simulated when the air input temperature was 38°C, depth of the

material bed was 1 m, and airflow direction switching time was 3 h

(Figure 6). The average temperature of the entire bed generally

increased after the start of the drying process. It rose rapidly at

the start of the drying process and then gradually slowed down

until it approached the air input temperature. During this process,

the average temperature dropped suddenly; however, it rose rapidly

during every other period of reversal. Thus, the heat was quickly

withdrawn from the dryer through the air, resulting in a rapid

decrease in the temperature of the entire bed. Then the injection

of the “new” air led to a rapid increase and recovery of the average

temperature of the entire bed[2,26]. The lower the air velocity, the

greater the drop in the average temperature.

Correspondingly, the change in average moisture content can

be roughly divided into two stages. First, the decreasing rate of

the average moisture content was almost the same, and the

difference of the moisture content of the bed material increased and

then decreased rapidly. Here, the moisture in the peanut hulls

rapidly evaporated from the bed under air heating. Second, the

rate of decrease of the average moisture content gradually

decreased. As the ventilation direction changes with time, the

changes in moisture content difference showed a wave-like pattern

with a gradual decrease in amplitude. In addition, the lower the

air velocity, the greater the difference of the moisture content.

Here, the outward migration and evaporation of moisture of the

peanut kernels played a dominant role.

a. Average temperature b. Average moisture content c. Moisture content difference

Figure 6 Simulation results of the overall drying process with different ventilation velocities. The ambient air temperature was 25°C and

humidity was 50%; material bed depth was 1 m, hot air input temperature was 38°C, and airflow reversing time was 3 h


3.1.3 Effects of air velocities and air direction switching time on

drying indices

Time consumption, thermal energy consumptions and moisture

content difference were calculated by the drying simulations when

the air input temperature was 38°C, the depth of the material bed

was 1 m, air velocity was 0.2 m/s, 0.3 m/s, 0.4 m/s, and 0.5 m/s,

and air direction switching time was 1 h, 2 h, 3 h, 4 h, and 5 h

(Figure 7). With the increase of air velocity, the time

consumption and moisture content difference decreased, and the

thermal energy consumed per unit mass increased significantly.

From 0.2 to 0.3 m/s, the moisture content difference decreased;

however, the decrease of moisture content difference was relatively

small when air velocity changed from 0.3 to 0.4 m/s and from

0.4 to 0.5 m/s. When the air direction switching time was 3 h, the

moisture content differences corresponding to air velocities of 0.3,

0.4, and 0.5 m/s were close.

a. Time consumption b. Moisture content difference c. Thermal energy consumption

Note: The ambient air temperature was 25°C, humidity was 50%, material bed depth was 1 m, and hot air input temperature was 38°C.

Figure 7 Drying indices at different air velocities and air direction switching times

In addition, when the air velocity remained constant, the air

direction switching time had little effect on the time consumption

and thermal energy consumed per unit mass; however, it had a

certain influence on the moisture content difference. An

appropriate air direction switching time was conducive to reducing

the moisture content difference. At an air velocity of 0.2 m/s, the

moisture content difference reached its minimum value when the

air direction switching time was 4 h; at an air velocity of 0.3 m/s,

the moisture content reached its minimum value when the air

direction switching time was 3 h; at an air ventilation velocity of

0.4 m/s, the moisture content difference reached its minimum value

when the air direction switching time was 2 h; and at an air velocity

of 0.5 m/s, the moisture content difference reached its minimum

value when the air direction switching time was 1 h. The larger

the air velocity, the smaller the best air direction switching time.

Combining time consumption, moisture content difference, and

thermal energy consumed per unit mass, when the ventilation

direction switching time was 3 h, the comprehensive operation

performance was better under different air velocities.

3.1.4 Stage division of segmented drying

Based on Figure 6, high temperature occurred at the later stage

of the drying process, thus maintaining the initial ventilation

velocity might cause a huge waste of energy. When the average

temperature is taken as the ordinate and the average moisture

content as the abscissa, a curve of temperature variation with

moisture content was obtained (Figure 8).

When the average moisture content was greater than 22%, the

average temperature fluctuated significantly with the average

moisture content. This stage occurred mainly during the rapid

heating at the beginning of the drying process. During the

following stage, the temperature of the material bed changed

steadily with decreasing average moisture content, and the

temperature drop amplitude caused by changing the ventilation

direction decreased gradually. Therefore, to reduce energy

consumption and improve heat utilization and uniformity of batch

drying, investigating segmented drying is considered indispensable.

The moisture content above 22% (wet basis) was taken as the first

stage. Meanwhile, the remaining drying stages were further

subdivided based on the variations of the average temperature.

Thus, moisture content of 14%-22% was taken as the second stage,

and a moisture content of 8%-14% was taken as the third stage.

Note: The ambient air temperature was 25°C and humidity was 50%; material

bed depth was 1 m, hot air input temperature was 38°C, and airflow reversing

time was 3 h.

Figure 8 Simulation results for variation of average temperature

with moisture content of the peanut bed

Four groups of ventilation velocities were then selected to

calculate the time consumption, moisture content difference, and

the thermal energy consumed per unit mass (Table 2). The results

showed that segmented drying could effectively reduce the

drying time and energy consumption and improve the drying

uniformity.

Table 2 Drying indices of segmented drying under different combinations of air velocities

No. Air velocity of different moisture content range/m·s

-1

Time consumption

/h

Moisture content

difference/%

Thermal energy consumption

/×106 J·kg

-1

40%-22% 22%-14% 14%-8%

1 0.3 0.3 0.3 46.9 0.58 3.56

2 0.3 0.3 0.2 47.9 0.56 3.12

3 0.4 0.3 0.3 43.7 0.54 3.59

4 0.4 0.3 0.2 44.7 0.56 3.17


3.1.5 Uniform experimental design and simulation results

To obtain the optimal ventilation parameter combination of

segmented drying, referring to previous research experience, the

ventilation velocity of the three drying stages was set between 0.2

and 0.5 m/s. A U13*(134) uniform design table was used to

perform a 3-factor 13-level uniform design series of simulations

with the indicators of the time consumption, moisture content

difference, and thermal energy consumed per unit mass[45]. Based

on this, a synthetic weighted mark was calculated. The

mathematical simulation parameters and results are presented in

Table 3.

Table 3 U13*(134) Uniform design arrangement and simulation results

No.

Air velocity of different moisture content ranges/m·s-1

Time consumption

/h

Moisture content

difference/%

Thermal energy

consumption

/(×106 J·kg

-1)

Synthetic weighted

mark Y* 40%-22%

X1

22%-14%

X2

14%-8%

X3

1 0.200(1) 0.400(9) 0.450(11) 50.7 1.13 4.55 8.01

2 0.225(2) 0.275(4) 0.375(8) 50.2 0.92 3.79 41.42

3 0.250(3) 0.500(13) 0.300(5) 48.0 0.73 4.19 41.44

4 0.275(4) 0.375(8) 0.225(2) 48.2 0.63 3.47 67.66

5 0.300(5) 0.250(3) 0.500(13) 45.6 0.61 4.15 53.51

6 0.325(6) 0.475(12) 0.425(10) 43.9 0.58 4.80 38.31

7 0.350(7) 0.350(7) 0.350(7) 44.3 0.55 3.92 66.55

8 0.375(8) 0.225(2) 0.275(4) 45.2 0.55 3.24 85.95

9 0.400(9) 0.450(11) 0.200(1) 43.9 0.54 3.62 77.60

10 0.425(10) 0.325(6) 0.475(12) 41.7 0.50 4.35 61.52

11 0.450(11) 0.200(1) 0.400(9) 42.6 0.49 3.70 80.33

12 0.475(12) 0.425(10) 0.325(6) 41.3 0.47 4.11 71.38

13 0.500(13) 0.300(5) 0.250(3) 42.4 0.45 3.49 89.06

Using the simulation results, a stepwise regression analysis

was performed. Non-significant items were eliminated, and the

regression model of the synthetic weighted mark with velocities for

three-stage drying was obtained (Equation (30)). The model

quality evaluation indices, including coefficient of determination

(R2), root mean squared error (RMSE), F value, and Sig. values are

presented in Table 4. The Sig. value for each significant item in

the regression equation is shown in Table 5. *

1 3 2 3

21

23.5398 603.109 27.9878 259.076

657.737

Y X X X X

X

(30)

where, Y* is the synthetic weighted mark; X1 is the velocity of the

first drying stage; X2 is the velocity of the second drying stage, and

X3 is the velocity of the third drying stage.

Table 4 Quality evaluations of the regression model

Index R2 RMSE F Sig.

Y* 0.987 3.22 152.154 1.40×10-6

Table 5 Significance level values of significant items for the

regression model

Items X1 X3 X2X3 X12

Sig. 0.0001 0.0485 0.0000 0.0004

The regression equation for the synthetic weighted mark Y* had

a coefficient of determination R2 > 0.98, showing that the regression

equation was in good agreement with the simulation data. The

significance test showed Sig. <0.01. Thus, the regression equation

has high reliability. Based on the Sig. value of each significant

item listed in Table 5, the order of the influence of each significant

item on the synthetic weighted mark was X2X3>X1>X12>X3. Thus,

the velocities in the three drying stages had a significant impact on

the synthetic weighted mark, and the interaction of velocities in the

second and third drying stages was significant.

3.1.6 Optimization of ventilation parameters

To solve the maximum value of the synthetic weighted mark

Y*, the minimum value of the opposite Y* was explored. The

boundary ranges of ventilation velocities in the three stages were

considered as three-factor constraint conditions.

Thus, the objective function is as follows:

Y = min(–Y*(X1, X2, X3)) (31)

with constraint conditions:

1

2

3

0.2 0.5

0.2 0.5

0.2 0.5

X

X

X

(32)

The “fmincon” function of Matlab software was used to solve

the above multiple linear constraint optimization equation. It was

concluded that when X1 = 0.46 m/s, X2 = 0.2 m/s and X3 = 0.2 m/s,

the Y value was the minimum, which was –98.75. Hence, Y* was

98.75, which was superior to all combinations of velocities shown

in Table 3. When X2 = X3, the ventilation velocities were the

same in the second and third drying stages, and the two stages

could be combined into one. Thus, the entire drying process can

be divided into two stages. At the start of drying, the optimal

ventilation velocity was 0.46 m/s. Then, when the average

moisture content dropped to 22%, the optimal ventilation velocity

was 0.2 m/s.

Taking the above ventilation velocities as the input values for a

reverse ventilation drying simulation of the peanut bed, the results

showed that the time consumption was 44.3 h, moisture content

difference was 0.51%, and thermal energy consumption per unit

mass of the dried material was 2.91×106 J/kg.

3.2 Validation of simulation by experimental results

Based on the optimization results in Section 3.1.5, and the

environmental and initial conditions of the materials during the

experiment, the temperature and moisture content changes of the

material bed were calculated through simulation. The material

bed was divided into three layers along the thickness direction, that

is, the upper, middle, and lower layers. The temperature and

moisture content of each layer were calculated, and the drying time

when the average moisture content of the entire bed reached 22%

wet basis was also calculated. The simulation results revealed


that when the average moisture content of the material bed reached

22% wet basis, drying time was 10.6 h; when the average moisture

content of the material bed reached 8% wet basis, the drying time

was 43.6 h. During experiments, a ventilation velocity of

0.46 m/s was used as the first stage for 0-10.6 h, and 0.2 m/s was

used as the second stage for 10.6-43.6 h. The temperatures of the

upper-, middle-, and lower-layer materials were recorded every 5 h.

The moisture contents of the upper-, middle-, and lower-layer

materials were measured after 15, 30, and 43.6 h of drying. The

simulation and experimental results were compared as Figure 9.

a. Temperature

b. Moisture content

Figure 9 Comparison between simulation and experimental

values for temperature and moisture content

The correlation coefficients of the simulation and experimental

values of temperature were 0.991, 0.989, and 0.993 for the upper,

middle, and lower layers of peanut, respectively. The correlation

coefficients of the simulation and experimental values of the

moisture content were 0.995, 0.994, and 0.988 for the upper-,

middle-, and lower-layer materials, respectively. The results,

therefore, showed that the simulations of temperature and moisture

content in different layers were good, and the simulation model

could accurately predict the reversing ventilation drying of peanuts.

3.3 Peanut quality after drying

Owing to the periodic change in the direction of the medium

air passing through the material bed during the reversing

ventilation drying, no material layers remain at the outlet in wet air

in the extended periods, which differs from conventional

unidirectional fixed-bed ventilation drying. After the validation

experiment (Section 2.5), no mildew was found in the dried peanuts.

Aflatoxin was not detected in five samples after reversing

ventilation drying and the three samples after natural sun drying

using the method specified in ISO Standard 16050[41], ISO

Standard 600[42], and ISO Standard 3960[43]. The acid and

peroxide values of the samples were determined. Taking the

average value as the final value, the results are listed in Table 6.

The acid and peroxide values of peanuts under reversing ventilation

drying were slightly higher than those under natural sun drying

(Section 2.5.3). The acid value of 0.18 mg/g was far below the

maximum acceptable value of 3 mg/g, and the peroxide value of

0.011 g/(100 g) was below the maximum acceptable value of

0.08 g/(100 g) set by the standard GB 19300[46]. These results

were consistent with those of peanuts dried in the southeastern

USA[13].

Table 6 Acid and peroxide value of peanut after drying

Items Acid value/mg·g-1

Peroxide value/g·(100 g)-1

Reversing drying 0.18 0.011

Natural drying 0.15 0.010

In addition, the flavors of dried peanuts were simply evaluated

by artificial tasting based on ISO Standard 6658[44]. The flavor of

peanuts after reversing ventilation was found to be good, and no

obvious rancid peanut was found. Thus, the taste of peanuts was

not significantly different from that of naturally dried peanuts.

4 Conclusions

The unevenness and energy consumption of batch drying can

be reduced by adopting reversing ventilation and segmented drying.

The quality of peanuts after reversing ventilation drying was found

to be close to that of natural sun drying. The optimal

comprehensive drying effect was obtained with a ventilation

velocity of 0.46 m/s when the average moisture content of peanut

materials was more than 22% and with a ventilation velocity of

0.20 m/s when the average moisture content was less than 22%.

The correlation coefficients of the simulation and experimental

results for the temperature and moisture content were above 0.98.

Thus, the simulation model developed could accurately describe

the reversing ventilation drying of peanuts.

Acknowledgments

This work was financially supported by the Special Expenses

for Basic Scientific Research of the Chinese Academy of

Agricultural Sciences (Grant No. S201937) and New Equipment

and New Technology Research, Development and Promotion

Project of Jiangsu Province Agricultural Machinery (Grant No.

SZ120180032).

Nomenclature

a Drying constant

as Specific surface area of peanut, m2·m

-3

b Drying constant

ca Specific heat of dry air, J/(kg·°C)

cv Specific heat of water vapor, J/(kg·°C)

cw Specific heat of liquid water, J/(kg·°C)

cpb Specific heat of bulk peanuts, J/(kg·°C)

Eco Energy consumption, J

Epum Energy consumption per unit mass, J/kg

mfinal Mass of peanut materials after drying, kg

h Height of material bed, m

hga Gasification heat of water in peanuts, J/kg

hT Heat transfer coefficient, W/(m·°C)

H Absolute humidity of air, kg/kg

Hin Absolute humidity of input air, kg/kg

jfinal Final iteration of time node j

k Drying constant

m Maximum node number of bed thickness


mfinial Mass of peanut materials after drying, kg

M Moisture content (dry basis) of material bed, kg/kg

M0 Initial moisture content (dry basis) of material bed, kg/kg

Me Equilibrium moisture content (dry basis) of peanut pods, kg/kg

Mdb Dry basis moisture content of peanut pods, %

Mun Moisture content difference (wet basis), %

n Maximum node number of drying time

RH Relative humidity of air, %

r Correlation coefficient

S Loading area, m2

t Drying time, h

tc Critical time of drying, h

teq Equivalent drying time, h

tfinal Final time consumption, h

T Air temperature, °C

Tam Ambient temperature, °C

Tin Input temperature of air, °C

Va Average velocity of air passing through the material bed, m/s

WI Weight of index I

x Depth in peanut bed from the bottom, m

X1 Velocity of the first drying stage, m/s

X2 Velocity of the second drying stage, m/s

X3 Velocity of the third drying stage, m/s

Y * Synthetic weighted mark

Y1, J Index value of Jth simulation values of the time consumed

Y2, J Index value of Jth simulation values of the moisture content

difference

Y3, J Index value of Jth simulation values of the energy consumption per

unit mas

Y**

I,J Mark of Ith index of Jth simulation results

Y*

I,J Index value of Ith index of Jth simulation results after unifying trend

Y*

I,max Maximum value of the Ith index after unifying trend

Y*

I,min Minimum value of the Ith index after unifying trend

Y*

J Synthetically weighted mark of Jth simulation results

ε Porosity of peanut bed

θ Temperature of the material layer, °C

θ0 Initial temperature of the material layer, °C

ρa Density of dry air, kg/m

3

ρA Density of wet air, kg/m

3

ρbf

Bulk density of peanut pods after drying, kg/m3

ρpb Bulk density of peanut bed, kg/m

33

uA Average velocity of wet air, m/s

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